The train runs directly from terminal 3, platform 2 to Copenhagen. It is a 2-minute walk from Copenhagen Central Station to the hotel.
If you take a taxi from the airport, it will cost around DKK 250,-. All taxis run on a meter and accept dankort and most major international credit cards.
Take the train from Østerport Station (southbound). Get off at Vesterport Station. You can see Imperial Hotel from there.